A group of students decides to sell pizzas to help raise money for their senior class trip. They sold a pepperoni pizza for $14, a sausage pizza for $11, and a cheese pizza for $10. At the end of their sales, the class sold a total of 400 pizzas and made $4560. The students sold 80 more cheese pizzas than pepperoni pizzas. How many of each type of pizza were sold?

The number of cheese pizza sold is 200 cheese pizzas

The number of sausage pizza sold is 80 sausage pizzas

The number of pepperoni pizza sold is 120 pepperoni pizzas

Step-by-step explanation:

The price at which the pepperoni  pizza was sold is $14

The price at which the sausage pizza was sold is $11

price at which the cheese pizza was sold is $10

The total number of pizzas sold = 400

The total amount made = $4560

The number of cheese pizza sold = 80 + the number of pepperoni pizzas

Let the number of cheese pizza sold = C

The number of sausage pizza sold = S

The number of pepperoni pizza sold = P

We have;

C + S + P = 400(1)

C = 80 + P(2)

10·C + 11·S + 14·P = $4560(3)

Substituting the value for C from equation (2) in equation (1), we get;

C + S + P = 400 = 80 + P + S + P = 400

2·P + S = 400 - 80 = 320

∴ S = 320 - 2·P(4)

Substituting the value for C from equation (2) and the value for S from equation (4) into equation (3), we get;

10·C + 11·S + 14·P = $4560

10·(80 + P) + 11·(320 - 2·P) + 14·P = 4560

800 + 10·P + 3,520 - 22·P + 14·P = 4560

4,320 + 2·P =  4560

2·P =  4560 - 4,320 = 240

P = 240/2 = 120

P = 120

C = 80 + P = 80 + 120 = 200

C = 200

S = 320 - 2·P = 320 - 2×120 = 320 - 240 = 80

S = 80

Therefore;

The number of cheese pizza sold = C = 200

The number of sausage pizza sold = S = 80

The number of pepperoni pizza sold = P = 120.